The rapper is performing an arena concert Saturday at London's O2 -- where he's doing two shows this weekend -- hitting the stage at around 9:30 PM local time. No introductions were needed ... TS just dove right into his set standing at the top of an elevated platform.

Trav was decked out in some futuristic costume with shades on ... and almost immediately, he cranked the energy level in the room up to 10 -- like he normally does for his shows.

After running through a couple songs up there, he made his way down ... where he kept the hype up. The audience seemed to be rocking with him all throughout. BTW  -- the place is absolutely packed, including in the nosebleeds ... and everyone looks to be vibing so far.

So far, nothing too crazy is going on. Yes ... Travis is screaming/jumping around, per usual, but he doesn't appear to be encouraging anyone to lose their minds beyond what they're already doing. He's literally just performing and staying in his element -- so it's all kosher.

Also ... Kylie Jenner and their daughter Stormi are present for Travis' big day. Trav just dedicated a song, "Mamacitas," to her, saying he knew she was there in the building.

Like we said, this is Travis' first solo performance of this scale since last November. He's obviously performed publicly since then -- in smaller venues and even via cameos at music festivals here in the U.S. -- but this is a big deal ... 'cause it's billed as strictly a Travis gig.

He's going to be headlining some other major events later this year -- including a festival in South America -- and he even has a Vegas residency all set up for him too next month.